I wrote last week about the origin of the multiplication symbol (x). It’s time to talk about other arithmetic operations.
The plus symbol (+) seems to have been used for the first time by the Frenchman Nicole d’Oresme (1323–1382) in the text “Reasons of Algorithms”, manuscript in Latin between 1356 and 1361. Originally, it was an abbreviation for the word “et” (“and” in Latin) but we do not know whether it was introduced by Oresme himself or by some copyist. The origin of the minus sign (–) is more uncertain: perhaps it is a simplification of the letter m (from “minus”).
The two symbols + and – were first printed in “Commercial Arithmetic”, published in 1489, by the German Johannes Widmann (1460–1498). But they were not referring to addition and subtraction operations, but to profit and loss in business. The first to use both as symbols of operations were the Dutchman Giel van der Hoecke, in 1514, and the German Henricus Grammateus (1495–1525), in 1518.
In the case of division, until today we use different symbols. A colon (:) was used in 1633 in a book titled “Johnson Arithmetic”. But there it was a fraction symbol: 3:4 meant “three quarters” and not the operation “divide three by four.” Half a century later, Gottfried Wilhelm Leibniz (1646-1716), who advocated that multiplication be represented by a dot, was using two dots for both fractions and the division operation.
The symbol ÷, the most used in English-speaking countries to represent division, was introduced by the Swiss Johann Rahn (1622-1676) in 1659. The diagonal bar / appeared in the 18th century as an alternative to the horizontal fraction bar, which is difficult to compose typographically. One of the first to use it was the English merchant Thomas Twinings (1675–1741), founder of the famous Twinings of London tea company, in a handwritten list of tea and coffee transactions dated 1718. Gradually, the symbol came into use also for the split operation.
The modern notation for potentiation, with the exponent represented by a superscript, was used by René Descartes (1596–1650) in the book “A Geometria”, published in 1637. Interestingly, he only used exponents greater than two, preferring to write aa in place of a2 (but always the3 not place of aaa).
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